Math Forum - Ask Dr. Math
You have formed a right triangle with legs of length l and w and hypotenuse of length n. Use the Pythagorean Theorem. n^2 = l^2 + w^2. To understand the difference between perimeter and area, think of perimeter as the length of To find the area of a rectangle, multiply the length by the width. Question The length and width of a rectangle are represented as But since we have established a relationship between the length and the width, we.
- Find the relationship between the length and width of certain rectangles diagonals?
- Measurement: Length, width, height, depth
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I looked up width in my dictionary, and it says "The measurement of the extent of something from side to side; the size of something in terms of its wideness. If I want "width" to mean across, I use "height," not length, for the other dimension. Or I can use definition a of length to mean I have to look at it from its OWN perspective, the length being the long dimension from its head to its tail, if it were an animal and the width being "from side to side" across its own length: If not, we have confusion.
The really bad case is in three dimensions. Does a rectangular prism have height, width, and length, or breadth, or depth, or - what do you call the dimension from front to back? We don't have any really good words for that. Eric Weisstein's World of Mathematics provides definitions of length, depth, height, and width: Depth Size The depth of a box is the horizontal Distance from front to back usually not necessarily defined to be smaller than the Width, the horizontal Distance from side to side.
Height The vertical length of an object from top to bottom. Width Size The width of a box is the horizontal distance from side to side usually defined to be greater than the Depth, the horizontal distance from front to back. Again, I don't know that this is a universally accepted definition, but I would tend to agree that width is horizontal, height is vertical, and length should not be used in combination with these; but when length and width are used together, it makes some sense to take length as the long dimension.
In other words, when length is used, it should be the long dimension, and position is irrelevant; when length is not mentioned, the dimensions are all relative to our perspective, and relative sizes are irrelevant. I think the statement of the problem was poorly worded, and should have been clarified, but their interpretation of it makes the best sense.
In particular, in talking about the shape of a rectangle, it's right to ignore position and ask for the ratio of its long to its short dimension, since that helps us recognize similar rectangles.
This would be even clearer if one of the three rectangles had been tilted 45 degrees!
As to how you're supposed to judge things like this when they don't tell you - to each his own. One of the things math teaches us is the importance of clarity in language, and the need to add extra words or special definitions to clarify what English leaves obscure.
Difference Between Length and Width
I wouldn't count wrong those who took width as horizontal I probably would have been one of them, before thinking this outbut I think this should be a memorable lesson for all of you.
I love seeing this kind of argument, because you can't really lose! Thanks so much for all that information! Actually, I told the students apparently incorrectlythat with the absence of clarity, I personally would have assumed that width is horizontal, and that length is I used the example of the doorway into the classroom, which has a window over its top.
The door is taller than it is "wide" there we go againand it occurred to me that if someone tried to bring something into the room that wouldn't fit horizontally, we would describe that object as being too "wide.
Area of a Rectangle
Did I confuse you with all that? It seems to me that when the only two words we have available to make our point are "width" and "length," we have to come up with one definition that works for all cases. I just naturally used the one where something doesn't fit through the door because it's too "wide.
Or something like that. Anyway, thanks for the help Have a good one! As I said, before I thought it through carefully I would have joined you in assuming that width means horizontal; and certainly in the context of an object fitting through a door, or of describing a window, that would be exactly right.
In these contexts the position of the rectangle is fixed, and it seems that the positional definition of width takes precedence in that case. Width as narrow dimension is applicable only in cases where the object itself is the frame of reference, where it is thought of as movable and is the focus of our attention. Is there a best way? There is more than one correct way! Any pair of these words can be used, as long as your words are used sensibly. If you use the word length, it should certainly be for the longest sides of the rectangle.
Measurement: Length, width, height, depth | Think Math!
Think of how you would describe the distance along a road: The words along, long, and length are all related. The distance across the road tells how wide the road is from one side to the other. That is the width of the road.
The words wide and width are related, too. When a rectangle is drawn "slanted" on the page, like thisit is usually clearest to label the long side "length" and the other side "width," as if you were labeling a road. If the rectangle is drawn with horizontal and vertical sides, people often use the word height to describe how high how tall the rectangle is. It is then perfectly correct to describe how wide the rectangle is from side to side by using the word width.
As you can see, when height and width are used together, either one can be greater. When the word height is used with base, it has a different meaning. Three dimensions We call the measure of athree-dimensional object its volume. Because edges are one-dimensional, and faces are two-dimensional, their measures are length and area, respectively.
As for naming the dimensions of a three-dimensional figure, the only rule is be sensible and clear. When the figure is "level," height if you use the word refers consistently to how tall the figure is, even if that dimension is greatest; length if you use the word refers to the longer of the other two dimensions.